Problem: Solve for $x$ and $y$ using elimination. ${5x+6y = 64}$ ${4x-5y = -37}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $-4$ and the bottom equation by $5$ ${-20x-24y = -256}$ $20x-25y = -185$ Add the top and bottom equations together. $-49y = -441$ $\dfrac{-49y}{{-49}} = \dfrac{-441}{{-49}}$ ${y = 9}$ Now that you know ${y = 9}$ , plug it back into $\thinspace {5x+6y = 64}\thinspace$ to find $x$ ${5x + 6}{(9)}{= 64}$ $5x+54 = 64$ $5x+54{-54} = 64{-54}$ $5x = 10$ $\dfrac{5x}{{5}} = \dfrac{10}{{5}}$ ${x = 2}$ You can also plug ${y = 9}$ into $\thinspace {4x-5y = -37}\thinspace$ and get the same answer for $x$ : ${4x - 5}{(9)}{= -37}$ ${x = 2}$